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arXiv · 2601.02781

On rates of convergence in central limit theorems of Selberg and Bourgade

Po-Han Hsu·Peng-Jie Wong
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Abstract

Based on the recent works of Radziwill-Soundararajan and Roberts, we establish a rate of convergence in Bourgade's central limit theorem for shifted Dirichlet $L$-functions. Our results also indicate that the dependence structure in the components of a random vector could have a dramatic impact on the rate of convergence in such a multivariate central limit theorem.

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Po-Han Hsu, Peng-Jie Wong. 2026-01-06. On rates of convergence in central limit theorems of Selberg and Bourgade. https://arxiv.org/abs/2601.02781

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